The proximity effect describes the extension of superconductivity into a metal, which is in contact with a superconductor. Scanning tunneling spectroscopy is used to probe this effect in a two-atomic-layer Pb/Ag nonsuperconducting film, surrounding a superconducting Pb nanoisland, with sub-nm spatial resolution. Here we show a nontrivial dependence of the length scales of the superconducting proximity effect on magnetic field. Surprisingly, we find that the magnetic field does not affect the induced superconductivity up to 0.3 T, but a breakdown of the proximity effect is induced for fields around 0.6 T, with a 1/H^p dependence with p ≅ 7. The unexpected robustness of the induced superconductivity in the presence of magnetic fields is ascribed to the high electronic diffusivity in the metallic wetting layer.